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Non-homogeneous Dirichlet boundary value problems in weighted Sobolev spaces |
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| Authors: | V Gol’dshtein D Motreanu VV Motreanu |
| Institution: | 1. Department of Mathematics, Ben Gurion University of the Negev, Be’er Sheva, 84105, Israel.;2. Département de Mathématiques, Université de Perpignan Via Domitia, Perpignan, 66860, France. |
| Abstract: | The paper presents existence and multiplicity results for non-linear boundary value problems on possibly non-smooth and unbounded domains under possibly non-homogeneous Dirichlet boundary conditions. We develop here an appropriate functional setting based on weighted Sobolev spaces. Our results are obtained by using global minimization and a minimax approach using a non-smooth critical point theory. |
| Keywords: | non-linear elliptic problem non-homogeneous Dirichlet boundary conditions weighted Sobolev spaces global optimization minimax principle |